Section error optimization method for internal thread of wide variable lead nut and computer storage medium

Abstract

The invention discloses a section error optimization method for an internal thread of a wide variable lead nut and a computer storage medium, and belongs to the technical field of ball screw pair internal thread grinders, the method comprises the following steps: 1, model establishment: establishing a theoretical model of the internal thread of the nut, a grinding wheel axial section model and a nut internal thread grinding model, and calculating a section error of the internal thread of the nut on the basis of the models; proposing a section error calculation model; 2, error analysis: analyzing the influence of the nut lead, the nominal diameter and the installation center distance on the section error; and step 3, optimization method proposing: proposing and implementing a section error optimization method aiming at a variable lead working condition, so that the section error is reduced. According to the invention, the machining precision can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of ball screw pair internal thread grinding machines, and more particularly to a truncation error optimization method for the internal thread of a wide variable lead nut and a computer storage medium. Background Art

[0002] As a key functional component of a precision transmission system, the performance of the ball screw pair directly affects the accuracy and stability of mechanical equipment. Domestic research in the field of ball screw pairs started late. Although some progress has been made in recent years, there are still deficiencies in the manufacturing process of high-precision, high-stability products. In particular, in the processing of wide variable lead nuts, truncation error control is a technical bottleneck. In the traditional form grinding method, the design accuracy of the grinding wheel truncation directly determines the processing accuracy of the inner raceway of the nut during the processing. Therefore, studying how to effectively reduce the truncation error and improve the processing accuracy is of great significance to improving the overall performance of the ball screw pair.

[0003] The processing of wide variable lead nuts is difficult, especially under variable lead conditions. The installation angle of the grinding wheel cannot always be consistent with the helix angle of the internal thread of the nut, resulting in increased truncation error.

[0004] Therefore, the existing processing methods have obvious deficiencies in controlling truncation errors, and a new optimization method is urgently needed to improve processing accuracy. Summary of the Invention

[0005] In view of this, the present invention provides a method for optimizing the truncation error of the internal thread of a wide variable lead nut and a computer storage medium. By establishing an accurate theoretical model and a calculation model, the influence of key parameters on the truncation error is systematically analyzed, and effective optimization measures are proposed.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for optimizing the truncation error of an internal thread of a wide variable lead nut comprises the following steps:

[0008] Step 1, model establishment: establishing a theoretical model of the internal thread of the nut, an axial truncation model of the grinding wheel, and a grinding model of the internal thread of the nut, and constructing a truncation error calculation model based on the theoretical model of the internal thread of the nut, the axial truncation model of the grinding wheel, and the grinding model of the internal thread of the nut;

[0009] Step 2, error analysis: using the truncation error calculation model, analyzing the influence of different parameters on the truncation error;

[0010] Step 3, optimization implementation: Based on the influence of the different parameters on the truncation error, for the variable lead working condition, combined with the preset truncation error optimization method, the truncation error is reduced.

[0011] Furthermore, the theoretical model is established in the following way:

[0012] The workpiece coordinate system, grinding wheel coordinate system and normal coordinate system are established with the nut center, grinding wheel center and ball center as the origin respectively;

[0013] Based on the double arc characteristics of the nut normal truncation, the theoretical equation of the right raceway is obtained as follows:

[0014]

[0015] Where p is the spiral parameter, P h is the lead of the internal thread of the nut, λ is the helix angle, r0 is the nominal radius, the eccentricity e1 and e2 are the eccentricities of the normal section and e1=(rd b / 2)cosα,e2=(rd b / 2)sinα, α is the contact angle, d b is the diameter of the ball, and μ is the arc angle of the raceway.

[0016] Furthermore, the axial truncation model of the grinding wheel is determined by the following formula:

[0017]

[0018] Where X, Y, and Z represent the coordinates of the grinding wheel section.

[0019] Furthermore, the grinding model is established by coordinate transformation, including:

[0020] Through the conversion of the grinding wheel coordinate system and the nut workpiece coordinate system, combined with the contact line expression between the grinding wheel rotating surface and the nut internal thread helical surface, the equation of the nut internal thread helical surface processed by the grinding wheel is obtained, and the expression is:

[0021]

[0022] At the same time, the coordinate transformation expression of the nut workpiece coordinate system to the internal thread normal coordinate system is:

[0023]

[0024] Where R is the grinding wheel radius corresponding to Z in the grinding wheel section, Z = f(R) is the mathematical expression of the grinding wheel section, is the angle between XOY plane and ON, λ is the helix angle, A is the grinding wheel installation center distance, Σ is the grinding wheel installation angle, and r0 is the nominal radius;

[0025] Combining the two equations, we can obtain the expression of the normal section of the helical surface of the internal thread of the nut.

[0026] Furthermore, the truncation error calculation model is constructed by the following steps:

[0027] Point A(z oi ,x oi ) is a discrete point on the theoretical truncated curve, where i = 1, 2, 3...n, and n is the number of discrete points;

[0028] Assume that point A′(z ri′ ,x ri′ ) is the point A on the theoretical truncation curve located on the coordinate axis x n The intersection point on the inverse truncation curve in the direction is is the truncation error corresponding to point A, and the length is represented by ΔL;

[0029] Point B(z ri ,x ri ) and point C(z ri+1 ,x ri+1 ) is to inversely find the two points on the truncated curve adjacent to the intersection point A′, where i = 1, 2, 3...m, and m is the number of discrete points;

[0030] According to point B(z ri ,x ri ) and point C(z ri+1 ,x ri+1 ) coordinates, the inverse truncation curve is fitted using the cubic spline curve fitting method, and the size of the truncation error ΔL of the nut internal thread is finally obtained:

[0031] ΔL=±|x ri′ -x oi |

[0032] In the formula, point A(z oi ,x oi ) is a discrete point on the theoretical truncated curve, where i = 1, 2, 3...n, n is the number of discrete points, assuming that point A′(z ri′ ,x ri′ ) is the point A on the theoretical truncation curve located on the coordinate axis x n The intersection point on the inverse truncation curve in the direction is is the truncation error corresponding to point A, and the length is represented by ΔL, where point B (z ri ,x ri ) and point C(z ri+1 ,x ri+1 ) is to inversely find two points on the truncated curve adjacent to the intersection point A′, where i = 1, 2, 3...m, and m is the number of discrete points.

[0033] Furthermore, the step 2, error analysis: using the truncation error calculation model, analyzes the influence of the lead, nominal diameter and installation center distance on the truncation error.

[0034] Furthermore, the preset truncation error optimization method includes: adjusting the grinding wheel truncation and grinding process parameters, and optimizing the grinding wheel installation angle so that the grinding wheel installation angle is consistent with the helix angle of the nut internal thread, thereby reducing the truncation error.

[0035] Further, optimization is achieved by integrating the Y-axis feed, A-axis deflection and grinding head installation mechanism, which includes:

[0036] A base is installed on the X-axis slide, and the Y-axis screw guide rail original is installed on the base. A set of direct-drive screw feed systems are respectively arranged on both sides of the base to form the Y1 axis and the Y2 axis, which respectively drive the Y1-axis slide and the Y2-axis slide to move. A turntable and a spindle slide are installed on both sets of slides, and a grinding head spindle box is installed on the spindle slide. When the positions of the two axes are synchronously controlled, the turntable, spindle slide and spindle box are driven to move along the Y-axis. When the Y1 axis is fixed and the Y2 axis is fed, the Y2-axis slide will drive the turntable, spindle slide and spindle box to rotate along the center line formed by the center plane of the electric spindle and the center plane of the Y1-axis screw to form the A-axis. At the same time, the rotation center coincides with the center of the grinding wheel to ensure that the grinding point position is constant when the installation angle is adjusted.

[0037] A computer storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for optimizing the truncation error of an internal thread of a wide-variable-lead nut.

[0038] It can be seen from the above technical solution that compared with the prior art, the present invention discloses a method for optimizing the truncation error of the internal thread of a wide variable lead nut and a computer storage medium. By establishing an accurate theoretical model and a calculation model, the influence of key parameters on the truncation error is systematically analyzed, and effective optimization measures are proposed, thereby avoiding the obvious deficiencies of the processing method in controlling the truncation error and improving the processing accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0040] Figure 1 This is a relationship diagram of several theoretical models involved before and after the present invention;

[0041] Figure 2 Schematic diagram of the coordinates of the nut raceway and the grinding wheel position in the theoretical model of the nut internal thread of the present invention;

[0042] Figure 3 This is a schematic diagram of the axial section of the grinding wheel of the present invention;

[0043] Figure 4 Schematic diagram of the truncation error calculation method of the present invention;

[0044] Figure 5 This is a comparison diagram of the normal grinding truncation of different nut leads when verifying the influence of the nut lead on the truncation error of the internal thread of the nut;

[0045] Figure 6 This is the designed grinding head mounting device and Y-axis structure diagram;

[0046] Figure 7 This is a comparison diagram of truncation errors after optimization according to the method of the present invention;

[0047] Figure 8(a) shows the reduction ratio of the truncation error of the variable lead nut in area a;

[0048] Figure 8(b) shows the reduction ratio of the truncation error of the overall variable lead nut;

[0049] Figure 9 Schematic diagram of the method of the present invention. DETAILED DESCRIPTION

[0050] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0051] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in this specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0052] Example 1:

[0053] See also Figure 9 The embodiment of the present invention discloses a method for optimizing the truncation error of the internal thread of a wide variable lead nut, the core of which is the following steps:

[0054] Step 1: Model establishment: Establish a theoretical model of the nut internal thread, a grinding wheel axial truncation model, and a nut internal thread grinding model. Based on the above models, a truncation error calculation model is proposed;

[0055] Step 2: Error analysis: Analyze the influence of nut lead, nominal diameter and installation center distance on truncation error;

[0056] Step 3: Optimization method proposed: for variable lead working conditions, a truncation error optimization method was proposed and implemented to significantly reduce the truncation error;

[0057] Specifically, wide variable lead ball screw nut is a fixed lead and variable lead ball screw nut with a wide lead range. According to the size of the lead and nominal diameter, it can be divided into micro lead nut, conventional lead nut and large lead nut. Among them, the nominal diameter d0≤12mm, the lead P h Nuts with a diameter of ≤3mm are called micro-lead nuts, with a nominal diameter of 16mm≤d0≤100mm and a lead of 4mm≤P h Nuts with a lead of ≤20 mm are called conventional lead nuts, with a nominal diameter of d0 ≥ 16 mm and a lead of d0 / 2 ≤ P h Nuts with a diameter of ≤d0 are called large lead nuts.

[0058] In a specific embodiment, the internal thread theoretical equation of the theoretical model of the nut internal thread is specifically:

[0059]

[0060] In a specific embodiment, the axial section of the grinding wheel in the established axial section model of the grinding wheel can be calculated by the formula:

[0061]

[0062] Where p is the spiral parameter, P h is the lead of the internal thread of the nut, λ is the helix angle, r0 is the nominal radius, the eccentricity e1 and e2 are the eccentricities of the normal section and e1=(rd b / 2)cosα,e2=(rd b / 2)sinα, α is the contact angle, d b is the diameter of the ball, μ is the raceway arc angle, and θ is the parameter of the thread helix.

[0063] In a specific embodiment, in the established nut internal thread grinding model, the expression of the helicoidal surface equation of the nut internal thread machined by the grinding wheel can be written as:

[0064]

[0065] At the same time, the coordinate transformation expression of the nut workpiece coordinate system to the internal thread normal coordinate system is:

[0066]

[0067] Where R is the grinding wheel radius corresponding to Z in the grinding wheel section, Z = f(R) is the mathematical expression of the grinding wheel section, is the angle between XOY plane and ON, λ is the helix angle, A is the grinding wheel installation center distance, Σ is the grinding wheel installation angle, and r0 is the nominal radius.

[0068] Combining the two equations, we can obtain the normal section expression of the helical surface of the internal thread of the nut.

[0069] In a specific embodiment, a method for calculating the truncation error is provided by using a truncation error calculation model. oi ,x oi ) is a discrete point on the theoretical truncated curve, where i = 1, 2, 3...n, (n is the number of discrete points), assuming that point A′(z ri′ ,x ri′ ) is the point A on the theoretical truncation curve located on the coordinate axis x n The intersection point on the inverse truncation curve in the direction is is the truncation error corresponding to point A, and the length is represented by ΔL. ri ,x ri ) and point C(z ri+1 ,x ri+1 ) are two points on the inverse truncation curve adjacent to the intersection point A′, where i = 1, 2, 3...m (m is the number of discrete points). Based on the coordinates of points B and C, the inverse truncation curve can be fitted using a cubic spline curve fitting method to ultimately determine the magnitude of the truncation error ΔL of the nut internal thread:

[0070] ΔL=±|x ri′ -x oi |

[0071] Specifically, the truncation error calculation model can systematically analyze the specific impact of different parameters on the truncation error.

[0072] In a specific embodiment, the optimization method of the present invention reduces the truncation error by adjusting the grinding wheel installation angle to keep it consistent with the helix angle of the internal thread of the nut.

[0073] Specifically, the present invention proposes a set of mechanisms integrating Y-axis feeding, A-axis deflection and grinding head installation, which realizes automatic adjustment of the grinding wheel installation angle and further improves the processing accuracy.

[0074] Specifically, the method is applicable to fixed lead and variable lead nuts of various leads.

[0075] Specifically, the present invention proposes a mechanism that integrates Y-axis feed, A-axis deflection, and grinding head installation. The mechanism includes a base mounted on an X-axis slide, on which components such as a Y-axis lead screw guide are mounted. A set of direct-drive lead screw feed systems are provided on either side of the base, forming the Y1 and Y2 axes, respectively, to drive the Y1-axis slide and the Y2-axis slide to move. A turntable and a spindle slide are mounted on both sets of slides, and a grinding head spindle box is mounted on the spindle slide. When the positions of the two axes are synchronously controlled, the turntable, spindle slide, and spindle box are driven to move along the Y-axis. When the Y1 axis is fixed and the Y2 axis is fed, the Y2-axis slide will drive the turntable, spindle slide, and spindle box to rotate along the center line formed by the center plane of the electric spindle and the center plane of the Y1-axis lead screw to form the A-axis, and the rotation center will coincide with the center of the grinding wheel.

[0076] On the other hand, a computer storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of a method for optimizing the truncation error of the internal thread of a wide variable lead nut are implemented.

[0077] Example 2:

[0078] See also Figure 1 The embodiment of the present invention provides a method for optimizing the truncation error of the internal thread of a wide variable lead nut, which specifically includes the following steps:

[0079] Step 1: Model establishment: Establish a theoretical model of the nut internal thread, a grinding wheel axial truncation model, and a nut internal thread grinding model. Based on the above models, a truncation error calculation model is proposed;

[0080] Step 2: Error analysis: Analyze the influence of nut lead, nominal diameter and installation center distance on truncation error;

[0081] Step 3: Optimization method proposed: For variable lead working conditions, a truncation error optimization method was proposed and implemented to reduce the truncation error by at least 37.2%.

[0082] See also Figure 2 Based on the fact that the intersection of the nut internal thread raceway and the normal plane at any point of the arc is an eccentric double arc, the nut center is used as the coordinate origin to establish the nut workpiece coordinate system o-xyz, the grinding wheel center is used as the origin to establish the grinding wheel coordinate system O-XYZ, and the ball center is used as the origin to establish the internal thread normal coordinate system o n -x n y n z n Since the normal section of the nut is a double arc and the left and right raceways are symmetrical, the following takes the right raceway as an example to solve the theoretical equation of the nut internal thread:

[0083]

[0084] Where p is the spiral parameter, P h is the lead of the internal thread of the nut, λ is the helix angle, r0 is the nominal radius, the eccentricity e1 and e2 are the eccentricities of the normal section and e1=(rd b / 2)cosα,e2=(rd b / 2)sinα, α is the contact angle, d b is the diameter of the ball, and μ is the arc angle of the raceway.

[0085] See also Figure 3 According to the principle of helicoidal machining, when a grinding wheel is grinding the internal threads of a nut, at any instant of relative motion, there is always a tangent contact line between the grinding wheel and the raceway being machined. The motion during machining is equivalent to the motion of the rotating surface and the helicoidal surface along their own axis. Therefore, when the contact line rotates around the axis of the grinding wheel shaft, the equation for the rotating surface of the grinding wheel is obtained, which is given by the following formula:

[0086] zn x +An y cotΣ+(A-x+pcotΣ)n z =0

[0087] Among them, n x 、n y 、n z The three normal vectors of the internal thread equation of the nut are obtained, from which the axial truncation of the grinding wheel in the axial truncation model of the grinding wheel in the present invention can be calculated by the formula:

[0088]

[0089] X, Y, Z represent the coordinates of the grinding wheel section, which is a coordinate of XYZ in the grinding wheel coordinate system O.

[0090] When the grinding wheel cross-section is known, the normal cross-section of the helical surface to be machined can be inversely calculated by analytical methods. By converting the grinding wheel coordinate system and the nut workpiece coordinate system, combined with the contact line expression between the grinding wheel rotating surface and the nut internal thread helical surface, the equation of the nut internal thread helical surface machined by the grinding wheel can be obtained:

[0091]

[0092] At the same time, the coordinate transformation expression of the nut workpiece coordinate system to the internal thread normal coordinate system is:

[0093]

[0094] Combining the two equations, we can obtain the normal section expression of the helical surface of the internal thread of the nut.

[0095] See also Figure 4In the truncation error calculation model of the present invention, the truncation error of the nut internal thread can be understood as the truncation error of a series of discrete points between the theoretical truncation and the ground truncation of the nut internal thread. Since the theoretical truncation and the number and position of the discrete points of the inverse truncation cannot be completely one-to-one corresponding, a calculation method for the truncation error is given. Point A(z oi ,x oi ) is a discrete point on the theoretical truncated curve, where i = 1, 2, 3...n, (n is the number of discrete points), assuming that point A′(z ri′ ,x ri′ ) is the point A on the theoretical truncation curve located on the coordinate axis x n The intersection point on the inverse truncation curve in the direction is is the truncation error corresponding to point A, and the length is represented by ΔL. ri ,x ri ) and point C(z ri+1 ,x ri+1 ) are two points on the inverse truncation curve adjacent to the intersection point A′, where i = 1, 2, 3...m (m is the number of discrete points). Based on the coordinates of points B and C, the inverse truncation curve can be fitted using a cubic spline curve fitting method to ultimately determine the magnitude of the truncation error ΔL of the nut internal thread:

[0096] ΔL=±|x ri′ -x oi |

[0097] In the formula, point A(z oi ,x oi ) is a discrete point on the theoretical truncated curve, where i = 1, 2, 3...n, n is the number of discrete points, assuming that point A′(z ri′ ,x ri′ ) is the point A on the theoretical truncation curve located on the coordinate axis x n The intersection point on the inverse truncation curve in the direction is is the truncation error corresponding to point A, and the length is represented by ΔL, where point B (z ri ,x ri ) and point C(z ri+1 ,x ri+1 ) are two points on the inverse truncated curve adjacent to the intersection point A′, where i = 1, 2, 3, ..., m, where m is the number of discrete points. Since the coordinates of point A′ may not exist on the inverse truncated curve, the coordinates of points B and C must be used to determine the specific coordinate location of point A′.

[0098] For details, see Figure 4According to the coordinates of point B and point C, the inverse truncation curve can be fitted using the cubic spline curve fitting method. The fitted inverse truncation curve equation can be expressed as:

[0099] z=a(xx ri ) 3 +b(xx ri ) 2 +c(xx ri )+d (1)

[0100] Where a, b, c, and d are the coefficients of the cubic spline fitting curve, and their specific sizes are related to the coordinate values of point B and point C.

[0101] Let the coordinate z of point A′ be oi′ Equal to the z coordinate of point A on the theoretical truncation curve oi , that is, z oi′ =z oi , and put it into formula (1) to find the specific coordinate value of point A′.

[0102] Known point A(z oi ,x oi ) and point A′(z ri′ ,x ri′ ) coordinates, the size of the truncation error ΔL of the nut internal thread can be calculated, that is:

[0103]

[0104] Because z oi′ =z oi , so formula (2) can be simplified as:

[0105] ΔL=±|x ri′ -x oi | (3)

[0106] Among them, "+" means that the inverse truncation curve is above the theoretical truncation curve, that is, the inverse truncation is enlarged compared with the theoretical truncation curve, and "-" means that the inverse truncation curve is below the theoretical truncation curve, that is, the inverse truncation is reduced compared with the theoretical truncation curve.

[0107] The truncation error calculation model provided by formula (3) can be used to calculate the truncation error of the normal truncation of the nut internal thread at different discrete points. By analyzing and calculating the truncation error, the maximum error of the truncation error ΔL can be obtained. max , minimum error ΔL min , average error These three indicators are used to evaluate the normal truncation error of the internal thread of the nut.

[0108] See also Figure 5This study examines the effects of nut lead, nut nominal diameter, and installation center distance on the truncation error of the nut's internal thread. This study only compares the normal grinding truncation errors for different nut leads. The results demonstrate a consistent pattern: As the nut lead increases, the truncation error increases; as the nut nominal diameter increases, the truncation error increases; and as the installation center distance increases, the truncation error decreases.

[0109] See also Figure 6 To implement the optimization method of the present invention, a mechanism integrating Y-axis feed, A-axis deflection, and grinding head installation has been designed. The mechanism includes a base mounted on the X-axis slide, onto which components such as the Y-axis lead screw guide are mounted. A set of direct-drive lead screw feed systems, forming the Y1 and Y2 axes, are installed on either side of the base, respectively, driving the Y1 and Y2 slides. A turntable and spindle slide are mounted on both slides, and the grinding head spindle box is mounted on the spindle slide. When the two axes are synchronously controlled, the turntable, spindle slide, and spindle box are driven to move along the Y-axis. When the Y1 axis is fixed and the Y2 axis is feeding, the Y2-axis slide drives the turntable, spindle slide, and spindle box to rotate along the centerline formed by the center plane of the electric spindle and the center plane of the Y1-axis lead screw, forming the A-axis, with the rotation center coinciding with the center of the grinding wheel. This device can be used to set the Y-axis in internal thread grinders for automatic measurement and offset of the large-lead grinding rod installation position. The grinding wheel can automatically offset a certain angle to meet the nut lead angle requirements.

[0110] Specifically, as shown in Table 1, the X-axis of the machine tool is responsible for the feed motion of the grinding head, with a total stroke of 300 mm. The roller linear guide pair is used as the guide element, the Rexroth MLP140 linear motor assembly is used as the drive element, and the Heidenhain LS-195S linear grating scale is used as the feedback element, thus forming a fully closed-loop position control system. The X-axis guide adopts MR55 specifications, and three V3-level heavy preloaded sliders are arranged on each side of the slide according to the size of the slide to obtain maximum stiffness and damping, which can minimize the grinding vibration. The guide pair adopts centralized lubrication. In order to minimize the influence of oil mist generated by the grinding process on the components, the X-axis slide adopts a fully enclosed structural design. The motor, grating scale and other components are separated from the processing area by the outer protective cover and the leather cavity armor protective covers at both ends, further improving the reliability of the machine tool. At the same time, other electrical pipelines installed on the upper part of the X-axis slide are led out by the fully enclosed drag chain after passing through the slide to avoid corrosion and aging of the cables.

[0111] The grinding head mounting device is installed on the X-axis slide and is used to complete the functions of grinding head clamping, grinding angle adjustment, and Z-axis grinding position adjustment. It mainly includes the spindle box, turntable, slide seat, base and other components. The spindle box is used for the installation of the grinding electric spindle. The structure of clamping the outer circle is adopted to ensure the installation accuracy of the electric spindle. The spindle box is installed on the turntable through a dovetail groove and can be manually adjusted and locked along the Z-axis direction of the machine tool to match the use requirements of grinding rods of different lengths. The turntable is installed on the slide and driven by the indexing screw. It can rotate a certain angle around the center of the ring groove. The rotation center is also the center of the dressing roller to ensure that the axial direction of the electric spindle is consistent with the lead angle of the nut being processed. The turntable is installed on the slide. The slide is connected to the slide seat through a precision dovetail structure. The manual adjustment of the slide in the Y direction of the machine tool is achieved by lifting the screw. It is mainly used for the application of eccentric grinding rods when processing large lead nuts.

[0112] Table 1 Parameters of grinding head installation device

[0113]

[0114]

[0115] See also Figure 7 After optimization using the method of the present invention, the truncation error generated by the variable lead nut when using the optimized grinding method in area b is larger than the truncation error generated by interference grinding, but both are within the range of 0.0016mm; in area a, the truncation error generated when using the optimized grinding method has a significant decreasing trend compared with the truncation error generated by interference grinding, and the overall level is within 0.0016mm, and is consistent with the truncation error in area b. The overall truncation error is more uniform than that generated by interference grinding.

[0116] Specifically, based on the principle of spiral surface processing, the present invention establishes a theoretical model of nut internal thread, a grinding wheel axial truncation model and a nut internal thread grinding model. On this basis, a calculation model for reducing truncation error is first innovatively proposed, see Figure 8(a)-Figure 8(b) To reduce the truncation error of variable-lead nuts, the authors systematically analyzed the influence of three key parameters—nut lead, nominal diameter, and installation center distance—on truncation error. Secondly, to address the truncation error issue under variable-lead conditions, they optimized the internal thread grinder's grinding wheel mounting structure and adjusted the mounting angle to match the nut's internal thread helix angle, reducing the truncation error by 37.2%. This invention not only significantly improves the transmission accuracy of ball screw pairs but also, through innovative improvements to the grinder structure, provides an effective solution for high-precision thread grinding, possessing significant engineering application value.

[0117] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0118] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing the truncation error of the internal thread of a wide variable lead nut, characterized in that: The following steps are involved: Step 1, model establishment: establishing a theoretical model of the internal thread of the nut, an axial truncation model of the grinding wheel, and a grinding model of the internal thread of the nut, and constructing a truncation error calculation model based on the theoretical model of the internal thread of the nut, the axial truncation model of the grinding wheel, and the grinding model of the internal thread of the nut; Step 2, error analysis: using the truncation error calculation model, analyzing the influence of different parameters on the truncation error; Step 3, optimization implementation: Based on the influence of the different parameters on the truncation error, for the variable lead working condition, combined with the preset truncation error optimization method, the truncation error is reduced.

2. A method for optimizing truncation error of internal threads of wide variable lead nuts according to claim 1, characterized in that: The theoretical model is established in the following way: The workpiece coordinate system, grinding wheel coordinate system and normal coordinate system are established with the nut center, grinding wheel center and ball center as the origin respectively; Based on the double arc characteristics of the nut normal truncation, the theoretical equation of the right raceway is obtained as follows: Where p is the spiral parameter, P h is the lead of the internal thread of the nut, λ is the helix angle, r0 is the nominal radius, the eccentricity e1 and e2 are the eccentricities of the normal section and e1=(rd b / 2)cosα, e2=(rd b / 2)sinα, α is the contact angle, d b is the diameter of the ball, and μ is the angle of the raceway arc.

3. The method for optimizing the truncation error of the internal thread of a wide-variable-lead nut according to claim 1, characterized in that: The axial truncation model of the grinding wheel is determined by the following formula: Where X, Y, and Z represent the coordinates of the grinding wheel section.

4. The method for optimizing the truncation error of the internal thread of a wide-variable-lead nut according to claim 1, characterized in that: The grinding model is established by coordinate transformation, including: Through the conversion of the grinding wheel coordinate system and the nut workpiece coordinate system, combined with the contact line expression between the grinding wheel rotating surface and the nut internal thread helical surface, the equation of the nut internal thread helical surface processed by the grinding wheel is obtained, and the expression is: At the same time, the coordinate transformation expression of the nut workpiece coordinate system to the internal thread normal coordinate system is: Where R is the grinding wheel radius corresponding to Z in the grinding wheel section, Z = f(R) is the mathematical expression of the grinding wheel section, is the angle between XOY plane and ON, λ is the helix angle, A is the grinding wheel installation center distance, Σ is the grinding wheel installation angle, and r0 is the nominal radius; Combining the two equations, we can obtain the expression of the normal section of the helical surface of the internal thread of the nut.

5. The method for optimizing the truncation error of the internal thread of a wide-variable-lead nut according to claim 1, characterized in that: The truncation error calculation model is constructed by the following steps: Point A(z oi ,x oi ) is a discrete point on the theoretical truncated curve, where i = 1, 2, 3...n, and n is the number of discrete points; Assume that point A′(z ri′ ,x ri′ ) is the point A on the theoretical truncation curve located on the coordinate axis x n The intersection point on the inverse truncation curve in the direction is is the truncation error corresponding to point A, and the length is represented by ΔL; Point B(z ri ,x ri ) and point C(z ri+1 ,x ri+1 ) is to inversely find the two points on the truncated curve adjacent to the intersection point A′, where i = 1, 2, 3...m, and m is the number of discrete points; According to point B(z ri ,x ri ) and point C(z ri+1 ,x ri+1 ) coordinates, the inverse truncation curve is fitted using the cubic spline curve fitting method, and the size of the truncation error ΔL of the nut internal thread is finally obtained: ΔL=±|x ri′ -x oi | In the formula, point A(z oi ,x oi ) is a discrete point on the theoretical truncated curve, where i = 1, 2, 3...n, n is the number of discrete points, assuming that point A′(z ri′ ,x ri′ ) is the point A on the theoretical truncation curve located on the coordinate axis x n The intersection point on the inverse truncation curve in the direction is is the truncation error corresponding to point A, and the length is represented by ΔL, where point B (z ri ,x ri ) and point C(z ri+1 ,x ri+1 ) is to inversely find two points on the truncated curve adjacent to the intersection point A′, where i = 1, 2, 3...m, and m is the number of discrete points.

6. The method for optimizing the truncation error of the internal thread of a wide-variable-lead nut according to claim 1, characterized in that: The step 2, error analysis: using the truncation error calculation model, analyzes the influence of the lead, nominal diameter and installation center distance on the truncation error.

7. The method for optimizing the truncation error of the internal thread of a wide-variable-lead nut according to claim 1, characterized in that: The preset truncation error optimization method includes: adjusting the grinding wheel truncation and grinding process parameters, and optimizing the grinding wheel installation angle to make the grinding wheel installation angle consistent with the helix angle of the nut internal thread, thereby reducing the truncation error.

8. The method for optimizing the truncation error of the internal thread of a wide-variable-lead nut according to claim 7, characterized in that: Optimization is achieved by integrating the Y-axis feed, A-axis deflection and grinding head mounting mechanism, which includes: A base is installed on the X-axis slide, and the Y-axis screw guide rail original is installed on the base. A set of direct-drive screw feed systems are respectively arranged on both sides of the base to form the Y1 axis and the Y2 axis, which respectively drive the Y1-axis slide and the Y2-axis slide to move. A turntable and a spindle slide are installed on both sets of slides, and a grinding head spindle box is installed on the spindle slide. When the positions of the two axes are synchronously controlled, the turntable, spindle slide and spindle box are driven to move along the Y-axis. When the Y1 axis is fixed and the Y2 axis is fed, the Y2-axis slide will drive the turntable, spindle slide and spindle box to rotate along the center line formed by the center plane of the electric spindle and the center plane of the Y1-axis screw to form the A-axis. At the same time, the rotation center coincides with the center of the grinding wheel to ensure that the grinding point position is constant when the installation angle is adjusted.

9. A computer storage medium, characterized in that The computer storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for optimizing the truncation error of an internal thread of a wide-variable-lead nut as claimed in any one of claims 1 to 8.

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